Optimist::TestSet::EllipticParaboloid< Real > Class Template Reference

Class container for the paraboloid function. More...

#include <EllipticParaboloid.hh>

Inherits Optimist::CostFunction< Real, 2, EllipticParaboloid< Real > >.

Public Types
using	Vector = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Vector
using	RowVector = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::RowVector
using	Matrix = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Matrix
Public Types inherited from Optimist::CostFunction< Real, 2, EllipticParaboloid< Real > >
using	Vector
using	RowVector
using	Matrix
Public Types inherited from Optimist::Function< Real, N, 1, EllipticParaboloid< Real > >
using	InputType
using	OutputType
using	FirstDerivativeType
using	SecondDerivativeType

Public Member Functions
	EllipticParaboloid ()
std::string	name_impl () const
void	evaluate_impl (const Vector &x, Real &out) const
void	first_derivative_impl (const Vector &x, RowVector &out) const
void	second_derivative_impl (const Vector &, Matrix &out) const
Public Member Functions inherited from Optimist::CostFunction< Real, 2, EllipticParaboloid< Real > >
	CostFunction ()
std::string	name () const
void	evaluate (const Vector &x, Vector &out) const
void	gradient (const Vector &x, RowVector &out) const
void	hessian (const Vector &x, Matrix &out) const
Public Member Functions inherited from Optimist::Function< Real, N, 1, EllipticParaboloid< Real > >
	Function ()
std::string	name () const
void	evaluate (const InputType &x, OutputType &out) const
void	first_derivative (const InputType &x, FirstDerivativeType &out) const
void	second_derivative (const InputType &x, SecondDerivativeType &out) const
constexpr Integer	input_dimension () const
constexpr Integer	output_dimension () const
const std::vector< InputType > &	solutions () const
const std::vector< InputType > &	guesses () const
const InputType &	solution (const Integer i) const
const InputType &	guess (const Integer i) const
bool	is_solution (const InputType &x, const Real tol=EPSILON_LOW) const

Private Attributes
Real	m_a {1.0}
Real	m_b {1.0}

Additional Inherited Members
Public Attributes inherited from Optimist::CostFunction< Real, 2, EllipticParaboloid< Real > >
friend	Function< Real, N, 1, CostFunction< Real, N, DerivedFunction > >
Protected Attributes inherited from Optimist::Function< Real, N, 1, EllipticParaboloid< Real > >
std::vector< InputType >	m_solutions
std::vector< InputType >	m_guesses

Detailed Description

template<typename Real>
class Optimist::TestSet::EllipticParaboloid< Real >

Class container for the paraboloid function, which is defined as:

$$f(\mathbf{x}) = ax^2 + by^2 \text{.}$$

The function has global minima at $\mathbf{x} = (0, 0)$, with $f(\mathbf{x}) = 0$. The initial guesses are generated on the square $x_i \in \left[-100, 100\right]$.

Template Parameters

Real	Scalar number type.

Member Typedef Documentation

Matrix

template<typename Real>

using Optimist::TestSet::EllipticParaboloid< Real >::Matrix = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Matrix

RowVector

template<typename Real>

using Optimist::TestSet::EllipticParaboloid< Real >::RowVector = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::RowVector

Vector

template<typename Real>

using Optimist::TestSet::EllipticParaboloid< Real >::Vector = typename CostFunction<Real, 2, EllipticParaboloid<Real>>::Vector

< Basic constants.

Constructor & Destructor Documentation

EllipticParaboloid()

template<typename Real>

Optimist::TestSet::EllipticParaboloid< Real >::EllipticParaboloid ( )

inline

Class constructor for the paraboloid function.

Member Function Documentation

evaluate_impl()

template<typename Real>

void Optimist::TestSet::EllipticParaboloid< Real >::evaluate_impl ( const Vector & x, Real & out ) const

inline

Compute the function value at the input point.

Parameters

[in]	x	Input point.
[out]	out	The function value.

first_derivative_impl()

template<typename Real>

void Optimist::TestSet::EllipticParaboloid< Real >::first_derivative_impl ( const Vector & x, RowVector & out ) const

inline

Compute the first derivative value at the input point.

Parameters

[in]	x	Input point.
[out]	out	The first derivative value.

name_impl()

template<typename Real>

std::string Optimist::TestSet::EllipticParaboloid< Real >::name_impl ( ) const

inline

Get the function name.

Returns

The function name.

second_derivative_impl()

template<typename Real>

void Optimist::TestSet::EllipticParaboloid< Real >::second_derivative_impl ( const Vector & , Matrix & out ) const

inline

Compute the second derivative value at the input point.

Parameters

[in]	x	Input point.
[out]	out	The second derivative value.

Member Data Documentation

m_a

template<typename Real>

Real Optimist::TestSet::EllipticParaboloid< Real >::m_a {1.0}

private

Coefficient $a$.

m_b

template<typename Real>

Real Optimist::TestSet::EllipticParaboloid< Real >::m_b {1.0}

private

Coefficient $b$.

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The documentation for this class was generated from the following file:

• include/Optimist/TestSet/CostFunction/EllipticParaboloid.hh